1. Field of the Invention
The present invention relates to a method for fitting third-degree Bezier curves to a series of data points. 2. Description of the Related Art
In the field of computer graphics, CAD (Computer Aided Design), outline font creation and the like, a third-degree Bezier curve P(t) represented by the following equation is used to express a contour of a character or a curve of a graphic pattern or the like: EQU P(t)=(1-t).sup.3 Q0+3(1-t).sup.2 tQ1+3(1-t)t.sup.2 Q2+t.sup.3 Q3 (0.ltoreq.t.ltoreq.1) (1)
where Q0 to Q3 are parameters (position vectors) for determining a figure and are also called control points. Note that Q0 and Q3 are start and end points, respectively, of the curve P(t) for 0.ltoreq.t.ltoreq.1.
In a technique for expressing a contour of a character or a graphic pattern by using a third-degree Bezier curve, for example, curve fitting to an original figure of a graphic pattern expressd in the form of a bit map is performed.
In this method, one Bezier curve is normally fitted on two points of start and end points Q0 and Q3 of a series of data points. A method for fitting a curve by using a Bezier curve is described in, e.g., Wolfgang BOHM, "A survey of curve and surface methods in CAGD", PP. 1 to 60, Computer Aided Geometric Design 1, 1984.
In this manner, in conventional curve fitting using a third-degree Bezier curve, two points are fitted by one curve. Therefore, if the number of fitting points is large, the number of control points Q0 to Q3 representing a Bezier curve is increased, thereby increasing the data amount to be processed.
Therefore, a method of fitting a third-degree Bezier curve on three or more points is needed.